A method and system for optimizing parameters of an LCC-S compensation network of a rotary ultrasonic machining system

Abstract

The present invention discloses a method and system for optimizing parameters of an LCC-S compensation network of a rotary ultrasonic machining system. The method is as follows: S1. Obtaining the equivalent parameter L of a loosely coupled transformer P , L S 、M PS 、R P and R S , and the equivalent electromechanical parameters L1, C1, R1, and C0 of the ultrasonic vibrator under variable load conditions; S2, construct an equivalent circuit model of the rotary ultrasonic machining RUM system including the LCC-S compensation network; S3, configure the LCC-S compensation network parameters; S4, use the RUM system frequency deviation, output power, and transmission efficiency under variable load conditions as the objective functions of the multi-objective optimization model; S5, use the no-load resonant frequency matching, design variable range, and compensation component stress as the constraints of the multi-objective optimization model; S6, determine the optimal combination of design variables and compensation network parameters. This invention effectively solves the problem of large resonant frequency deviation of traditional static compensation networks under variable load conditions and significantly improves the load adaptability of the LCC-S compensation network.

Description

Technical Field

[0001] The present invention belongs to the technical field of non-contact energy transmission, and in particular relates to a method and system for optimizing LCC-S compensation network parameters of a rotary ultrasonic machining system. Background Art

[0002] In rotary ultrasonic machining (RUM) systems, energy transmission methods are primarily categorized as contact energy transmission and contactless energy transmission (CET). CET technology requires no physical contact and offers advantages such as wear-free operation, high rotational speed, and high reliability, making it widely used in RUM systems.

[0003] During rotary ultrasonic machining, the resonant frequency of the ultrasonic vibrator will drift as the load changes. This is mainly due to the dynamic changes in the impedance characteristics of the ultrasonic vibrator caused by the load change. In order to maintain the optimal working state of the ultrasonic vibrator under variable load conditions, the ultrasonic power supply needs to detect and track the resonant frequency of the ultrasonic vibrator in real time. Due to the introduction of CET technology, the ultrasonic power supply cannot directly detect the resonant frequency of the ultrasonic vibrator through the brush. The existing detection method usually uses a compensation network to achieve resonant frequency matching between the RUM system and the ultrasonic vibrator, so that the ultrasonic power supply can indirectly detect the resonant frequency of the ultrasonic vibrator by monitoring the resonant frequency of the RUM system, thereby realizing dynamic tracking of the resonant frequency. In addition, the compensation network can also effectively compensate for the leakage inductance of the loosely coupled transformer and the reactance of the ultrasonic vibrator, achieving efficient power transmission and electroacoustic energy conversion.

[0004] Traditional static compensation networks fail to consider the impact of load variations on the ultrasonic transducer's impedance characteristics during design. This results in an inability to adapt to resonant frequency matching under variable load conditions, leading to a resonant frequency deviation between the RUM system and the ultrasonic transducer. This deviation significantly increases with increasing load. This deviation not only directly affects the ultrasonic power supply's output characteristics but also significantly reduces the ultrasonic transducer's amplitude.

[0005] To address this issue, researchers have proposed dynamic compensation methods, which adjust compensation component parameters in real time to adapt to load changes. While this approach is effective in addressing load variations, it also places higher demands on the design and automatic control of the compensation network, while also increasing system complexity and cost. Therefore, designing a static compensation network that can effectively cope with load variations has become a more ideal solution.

[0006] In recent years, high-order compensation networks, which increase design freedom by introducing additional compensation components, have attracted widespread attention. By optimizing the parameters of the high-order compensation network, such networks can reduce the system's sensitivity to load variations.

[0007] Therefore, in response to the challenges brought by load changes in rotary ultrasonic machining, developing an effective static compensation network and its parameter design method has become a key issue that needs to be solved urgently in this field. Summary of the Invention

[0008] The present invention expands the optimization space of LCC-S compensation network parameters by introducing dual design variables, and proposes a dual design variable multi-objective optimization model for RUM system under variable load conditions. The model takes the resonant frequency deviation, transmission efficiency and output power of the system under variable load conditions as objective functions, aiming to improve the load adaptability of the compensation network. In particular, the model focuses on the constraints of the stress of the compensation components under variable load conditions to ensure the reliability of the system in practical applications. In order to obtain the optimal combination of design variables, the third-generation non-dominated sorting genetic algorithm (NSGA-III) is used to globally optimize the design variables, and then obtain the Pareto solution set. Finally, the optimal solution is screened out from the Pareto solution set based on the ideal point method, and the optimal LCC-S compensation network parameters are determined. The present invention effectively solves the problem of large resonant frequency deviation of traditional static compensation networks under variable load conditions, and significantly improves the load adaptability of the LCC-S compensation network.

[0009] The technical solutions of the present invention are as follows:

[0010] A method for optimizing parameters of an LCC-S compensation network of a rotary ultrasonic machining system comprises the following steps:

[0011] S1. Obtain the equivalent parameter of the loosely coupled transformer, the primary self-inductance L P , secondary side self-inductance L S 、Mutual inductance PS , equivalent internal resistance R P And the equivalent internal resistance R S , as well as the equivalent electromechanical parameters of the ultrasonic vibrator under variable load conditions, dynamic inductance L1, dynamic capacitance C1, dynamic resistance R1 and static capacitance C0, providing parameter support for subsequent system modeling and optimization;

[0012] S2, constructing an equivalent circuit model of the rotary ultrasonic machining RUM system including the LCC-S compensation network;

[0013] S3. Configure LCC-S compensation network parameters;

[0014] S4, taking the RUM system frequency deviation, output power, and transmission efficiency under variable load conditions as the objective functions of the multi-objective optimization model;

[0015] S5. No-load resonant frequency matching, design variable range, and compensation component stress are used as constraints for the multi-objective optimization model.

[0016] S6. Determine the optimal design variables β1 and β2, and determine the optimal compensation network parameter combination.

[0017] In the present invention, the RUM system can adopt the following structure: it includes an ultrasonic power supply, an LCC-S compensation network, a loosely coupled transformer, an ultrasonic vibrator and a tool, wherein the LCC-S compensation network is composed of the compensation inductance L of the primary compensation network. f , the first compensation capacitor C f , the second compensation capacitor C P , and the third compensation capacitor C of the secondary compensation network S The loosely coupled transformer is composed of a primary magnetic core and coil, a secondary magnetic core and coil, and its equivalent parameters include the primary self-inductance L P , Primary coil equivalent internal resistance R P , secondary side self-inductance L S , secondary coil equivalent internal resistance R S 、Mutual inductance PS and coupling coefficient K. The ultrasonic vibrator is composed of a piezoelectric ultrasonic transducer and a horn, and its equivalent circuit is composed of a static branch and a dynamic branch in parallel. The static branch includes a static capacitor C0, and the dynamic branch is composed of a dynamic inductor L1, a dynamic capacitor C1 and a dynamic resistor R1 in series. The compensation inductor L f One end is connected to the output end of the ultrasonic power supply, and the other end is connected to the first compensation capacitor C f and the second compensation capacitor C P The second compensation capacitor C P connected in series with the primary coil; the third compensation capacitor C S One end is connected to the secondary coil, and the other end is connected to the ultrasonic vibrator.

[0018] The ultrasonic power supply transmits energy to the primary coil of a loosely coupled transformer via a primary compensation network, generating an alternating magnetic field. This alternating magnetic field is then transmitted to the secondary coil via magnetic coupling, inducing voltage and current in the secondary coil. The secondary current then flows through the secondary compensation network to power the ultrasonic transducer, achieving energy transmission and electroacoustic conversion.

[0019] Preferably, step S2 is as follows:

[0020] S2.1, construct a structure including the third compensation capacitor C S The secondary side equivalent circuit model connected in series, the equivalent impedance Z of the secondary side equivalent circuit is obtained S The expression is:

[0021]

[0022] Where j represents the imaginary unit, R t represents the equivalent resistance of the ultrasonic vibrator, X trepresents the equivalent reactance of the ultrasonic vibrator, ω is the operating angular frequency;

[0023] In the secondary side equivalent circuit model, when the system operating angular frequency ω is equal to the ultrasonic vibrator series resonance angular frequency ω s When they are equal, the impedance of the ultrasonic vibrator is minimum and the amplitude is maximum. s and the corresponding resonant frequency f s for:

[0024]

[0025] S2.2. Establish the primary side equivalent circuit model including the LCC-S compensation network and obtain the input impedance Z in The expression is:

[0026]

[0027] Among them, X r is the reflected reactance, R r is the reflected resistance.

[0028] Preferably, step S3, configuring the LCC-S compensation network parameters, is as follows:

[0029] S3.1. Substitute equation (2) into equation (1) to derive the third compensation capacitor C S Satisfy the secondary circuit resonance condition Im(Z s )=0 is:

[0030]

[0031] Among them, Im represents the imaginary part;

[0032] S3.2, replace L in the primary equivalent circuit P 、C P 、R P and R r The branch formed is equivalent to an RLC series branch, and its equivalent impedance is Z1. s C that achieves resonance at P The value is recorded as C P1 ; Introduce the first design variable β1 and define C P The actual value of is:

[0033] C P =β1C P1 (5)

[0034] in,

[0035] S3.3, set the first compensation capacitor C fThe equivalent impedance connected in parallel with the RLC series branch is denoted as Z2, and its expression is:

[0036]

[0037] In order for the equivalent impedance Z2 to be purely resistive, the condition β1>1 must be satisfied.

[0038] S3.4. Obtain the first compensation capacitor C that satisfies the resonance condition Im(Z2)=0 f The value of C f1 , and introduce the second design variable β2 to adjust the compensation capacitor C f The actual value of

[0039] C f =β2C f1 (7)

[0040] in,

[0041] S3.5, input impedance Z in By compensating inductor L f The inductive reactance is connected in series with the equivalent impedance Z2. in Showing pure resistance, L f The value should satisfy the following relationship:

[0042]

[0043] Among them, to ensure L f The value of is positive and must satisfy the condition β2>1.

[0044] Preferably, step S4 uses the RUM system frequency deviation, output power, and transmission efficiency under variable load conditions as objective functions in the multi-objective optimization model; specifically, as follows:

[0045] S4.1. Based on the resonance condition of the primary equivalent circuit, the resonant frequency f of the RUM system is obtained. r1 The relationship between

[0046] set up and According to formula (3), the resonance condition of the primary equivalent circuit can be deduced as follows:

[0047]

[0048] Where Im represents the imaginary part;

[0049] In step S1, L P , L S 、M PS 、R P and RS The specific value of has been determined, the resonant angular frequency ω of the system r1 and the resonant frequency f r1 The compensation network parameters and the reflected impedance Z r Decide;

[0050] S4.2. Calculate the resonant frequency f of the RUM system under m load conditions r1 The resonance frequency f of the ultrasonic vibrator in series s The average frequency deviation between them is used as the evaluation function F1:

[0051]

[0052] Among them, f r1 (i) represents the resonant frequency of the RUM system under the i-th load condition, f s (i) represents the series resonant frequency of the ultrasonic vibrator under the i-th load condition;

[0053] S4.3. Based on Kirchhoff's current law, the current expression of each branch is obtained as shown in formula (11), and the output power P is obtained t The expression of transmission efficiency η is shown in formula (12);

[0054]

[0055] Among them, I in Indicates the system input current, U in Indicates the input voltage, I f Represents the current flowing through the first compensation capacitor, I P Represents the current flowing through the primary coil, I S Represents the current flowing through the ultrasonic vibrator;

[0056]

[0057] S4.4, at input voltage U in is 50V and the operating frequency is f r1 Under the condition of m load conditions, the average output power is calculated as the evaluation function F2, and the expression is:

[0058]

[0059] Among them, P t (i) represents the output power of the RUM system under the i-th load condition;

[0060] S4.5. Calculate the average transmission efficiency of the RUM system under m load conditions as the evaluation function F3, which is expressed as:

[0061]

[0062] Where η(i) represents the transmission efficiency of the RUM system under the i-th load condition;

[0063] The evaluation function model is obtained as:

[0064]

[0065] Preferably, step S5 uses no-load resonant frequency matching, design variable range, and compensation component stress as constraints in the multi-objective optimization model; specifically, as follows:

[0066] No-load resonant frequency matching constraint: Under no-load conditions, i = 1, the RUM system is required to achieve resonant frequency matching with the ultrasonic vibrator, and the compensation network parameters must meet the constraint Im(Z in [ω s (i=1)])=Im(Z s [ω s (i=1)])=0;

[0067] Design variable range constraints; in order to achieve a wide range of parameter space in the optimization process and comprehensively consider cost factors, set the compensation capacitor C P and C f The value range of is 0-500nF, and the corresponding design variables are defined as 1<β1<8.4, 1<β2<55.5;

[0068] Compensation component stress constraints; based on the working conditions of variable load and ultrasonic vibrator maximum power of 400W, set the rated voltage U of the compensation capacitor max The maximum allowable current of the compensation inductor is 800V. max is 8A; the stress constraint function of the compensation element is:

[0069]

[0070] Among them, I Lf (i) is the current stress of the compensation inductor under the i-th load condition, U Cf (i) is the voltage stress of the first compensation capacitor under the i-th load condition, U CP (i) is the voltage stress of the second compensation capacitor under the i-th load condition, U Cs (i) is the voltage stress of the third compensation capacitor under the i-th load condition.

[0071] Preferably, step S6 is to determine the optimal design variables β1 and β2, and determine the optimal compensation network parameter combination. Specifically, the following are the steps:

[0072] The NSGA-III algorithm combines non-dominated sorting and reference point allocation to improve optimization performance and stability while maintaining solution diversity and uniform distribution. It is particularly suitable for high-dimensional multi-objective optimization problems.

[0073] The NSGA-III algorithm generates a uniformly distributed Pareto solution set that reflects the non-dominated solutions and trade-off relationships between different objectives;

[0074] The ideal point method is used to evaluate the Pareto solution set. The steps are as follows: select the optimal normalized value of each objective function from all solutions as the ideal point, calculate the Euclidean distance between the i-th candidate solution and the ideal point, and select the candidate solution closest to the ideal point as the optimal solution. The mathematical expression is:

[0075]

[0076] Where y i represents the Euclidean distance between the i-th candidate solution and the ideal point, is the normalized value of the ideal point of the j-th target, is the normalized value of the i-th candidate solution on the j-th index;

[0077] The optimal design variables and LCC-S compensation network parameters are determined through the optimal solution.

[0078] The present invention also discloses a LCC-S compensation network parameter optimization system for a rotary ultrasonic machining system, which is used to execute the above method and includes the following modules:

[0079] Equivalent parameter acquisition module: obtain the equivalent parameter primary side self-inductance L of the loosely coupled transformer P , secondary side self-inductance L S 、Mutual inductance PS , equivalent internal resistance R P And the equivalent internal resistance R S , as well as the equivalent electromechanical parameters of the ultrasonic vibrator under variable load conditions: dynamic inductance L1, dynamic capacitance C1, dynamic resistance R1 and static capacitance C0;

[0080] RUM system equivalent circuit model construction module: Constructs the RUM system equivalent circuit model including the LCC-S compensation network;

[0081] Compensation network parameter configuration module: configure LCC-S compensation network parameters;

[0082] Objective function determination module: The RUM system frequency deviation, output power, and transmission efficiency under variable load conditions are used as the objective functions of the multi-objective optimization model;

[0083] Constraint determination module: uses no-load resonant frequency matching, design variable range, and compensation component stress as constraints for the multi-objective optimization model;

[0084] Optimal parameter solving module: Determine the optimal design variables and solve the global optimal compensation parameter combination.

[0085] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0086] Under the premise of keeping the LCC-S compensation network structure unchanged, the present invention makes full use of its inherent multi-design freedom characteristics and proposes a compensation network parameter configuration method based on dual design variables, thereby providing greater optimization potential for the LCC-S compensation network.

[0087] This paper also proposes a dual-design variable, multi-objective optimization model for RUM systems under variable load conditions. It uses the third-generation non-dominated sorting genetic algorithm (NSGA-III) and the ideal point method to determine the optimal LCC-S compensation network parameters. While ensuring system reliability, this paper effectively addresses the large resonant frequency deviation problem of traditional static compensation networks under variable load conditions, enhances the load adaptability of the LCC-S compensation network, and significantly improves transmission efficiency and output power under heavy load conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 It is a structural schematic diagram of a rotary ultrasonic machining system;

[0089] Figure 2 for Figure 1 Equivalent circuit model of

[0090] Figure 3 is the equivalent circuit model of the ultrasonic vibrator;

[0091] Figure 4 for Figure 2 A simplified form of the equivalent circuit model is shown;

[0092] Figure 5 It is a schematic diagram of the RLC series branch and parallel resonant circuit;

[0093] Figure 6 Schematic diagram of the optimization process of the NSGA-III algorithm;

[0094] Figure 7 This is a diagram of the Pareto solution set;

[0095] Figure 8(a) is a comparison of the experimental data of the frequency deviation index before and after the optimization of the LCC-S compensation network;

[0096] Figure 8(b) is a comparison of the experimental data of the output power indicators before and after the optimization of the LCC-S compensation network;

[0097] Figure 8(c) is a comparison of experimental data of transmission efficiency indicators before and after optimization of the LCC-S compensation network;

[0098] Figure 9 It is a block diagram of a LCC-S compensation network parameter optimization system for a rotary ultrasonic machining system according to a preferred embodiment of the present invention.

[0099] Figure 1 In the figure, 1-ultrasonic power supply; 2-primary compensation network; 3-primary magnetic core; 4-primary coil; 5-air gap; 6-ultrasonic tool handle; 7-secondary coil; 8-secondary magnetic core; 9-secondary compensation network; 10-ultrasonic vibrator; 11-tool. DETAILED DESCRIPTION

[0100] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0101] This embodiment provides a method for optimizing the parameters of the LCC-S compensation network of a rotary ultrasonic machining system. The RUM system involved in this embodiment is composed of an ultrasonic power supply, an LCC-S compensation network, a loosely coupled transformer, an ultrasonic vibrator, and a tool. The LCC-S compensation network includes a compensation inductor L f , the first compensation capacitor C f , the second compensation capacitor C P and the third compensation capacitor C S The loosely coupled transformer is composed of a primary magnetic core and coil, a secondary magnetic core and coil, and its equivalent parameters include the primary self-inductance L P , equivalent internal resistance R P , secondary side self-inductance L S , equivalent internal resistance R S 、Mutual inductance PS and coupling coefficient K. The ultrasonic vibrator includes a piezoelectric ultrasonic transducer and a horn, and its equivalent circuit is composed of a static branch and a dynamic branch in parallel. The static branch includes a static capacitor C0, and the dynamic branch is composed of a dynamic inductor L1, a dynamic capacitor C1 and a dynamic resistor R1 in series. The compensation inductor L f One end is connected to the output end of the ultrasonic power supply, and the other end is connected to the first compensation capacitor C f and the second compensation capacitor C P The second compensation capacitor C P connected in series with the primary coil; the third compensation capacitor C S One end is connected to the secondary coil, and the other end is connected to the ultrasonic vibrator.

[0102] Specifically, Figure 1The figure shows a schematic diagram of the RUM system. The ultrasonic power supply transmits energy to the primary coil of a loosely coupled transformer through a primary compensation network, generating an alternating magnetic field. This alternating magnetic field is then transmitted to the secondary coil through magnetic coupling, inducing voltage and current in the secondary coil. The secondary current then flows through the secondary compensation network to power the ultrasonic transducer, achieving energy transmission and electroacoustic conversion.

[0103] This embodiment provides a method for optimizing parameters of an LCC-S compensation network of a rotary ultrasonic machining system, specifically comprising the following steps:

[0104] S1. Use LCR bridge to obtain the equivalent parameter L of loosely coupled transformer P , L S 、M PS 、R P and R S , as shown in Table 1; at the same time, the equivalent electromechanical parameters L1, C1, R1 and C0 of the ultrasonic vibrator under variable load conditions are obtained using an impedance analyzer;

[0105] Table 1. Equivalent parameters of loosely coupled transformers

[0106]

[0107] S2. Construct an equivalent circuit model of the RUM system including the LCC-S compensation network;

[0108] S2.1, construct a structure including the third compensation capacitor C S The secondary side equivalent circuit model connected in series, the equivalent impedance Z of the secondary side equivalent circuit is obtained S expression:

[0109] like Figure 2 Shown Figure 1 The equivalent circuit model includes the primary side equivalent circuit and the secondary side equivalent circuit. In the secondary side equivalent circuit, when the system operating angular frequency ω is equal to the ultrasonic vibrator series resonance angular frequency ω s When the values ​​of the dynamic branch are equal, the dynamic branch is purely resistive, and the impedance of the ultrasonic vibrator reaches its minimum and the amplitude reaches its maximum. s and the corresponding resonant frequency f s They are:

[0110]

[0111] like Figure 3 As shown, the ultrasonic vibrator equivalent impedance Z t Can be decomposed into equivalent resistance R t and equivalent reactance X t Indicates that its expressions are:

[0112]

[0113] Substituting equation (1) into equation (2), the equivalent impedance of the ultrasonic vibrator at the series resonant frequency can be obtained as:

[0114]

[0115] Here, j represents the imaginary unit.

[0116] From formula (3), we can see that the ultrasonic vibrator shows capacitive characteristics at the series resonant frequency. In order to improve the impedance characteristics between the ultrasonic vibrator and the secondary circuit, a third compensation capacitor C is connected in series with the secondary circuit. S Tuning is performed. At this time, the equivalent impedance Z of the secondary circuit S It can be expressed as:

[0117]

[0118] S2.2. Establish the primary side equivalent circuit model including the LCC compensation network and obtain the input impedance Z in The expression of is shown in formula (6);

[0119] In coupled circuit analysis, the reflected impedance Z r Used to characterize the secondary side impedance Z S Input impedance Z in The impact of Figure 4 As shown. Reflected impedance Z r Can be decomposed into the reflected resistance R r and reflected reactance X r , which is expressed as follows:

[0120]

[0121] By analyzing the primary side equivalent circuit including the primary side LCC compensation network, the input impedance Z of the RUM system is derived. in , which is expressed as follows:

[0122]

[0123] S3. Configure LCC-S compensation network parameters;

[0124] S3.1. Substitute equation (1) into equation (4) to obtain the third compensation capacitor C S Satisfy the secondary circuit resonance condition Im(Z s )=0 is:

[0125]

[0126] Here, Im represents the imaginary part.

[0127] S3.2, as shown in Figure (5), replace the primary side equivalent circuit with L P 、C P 、R P and R r The branch formed is equivalent to an RLC series branch, and its equivalent impedance is Z1. s C that achieves resonance at P The value is recorded as C P1 ; Introduce the first design variable β1 and define C P The actual value of is:

[0128] C P =β1C P1 (8)

[0129] in,

[0130] S3.3, set the first compensation capacitor C f The equivalent impedance connected in parallel with the RLC series branch is denoted as Z2, and its expression is:

[0131]

[0132] In order for the equivalent impedance Z2 to be purely resistive, the condition β1>1 must be satisfied.

[0133] S3.4. Obtain the first compensation capacitor C that satisfies the resonance condition Im(Z2)=0 f The value of C f1 , and introduce the second design variable β2 to adjust the compensation capacitor C f The actual value of

[0134] C f =β2C f1 (10)

[0135] in,

[0136] S3.5, input impedance Z in By compensating inductor L f The inductive reactance is connected in series with the equivalent impedance Z2. in Showing pure resistance, L f The value should satisfy the following relationship:

[0137]

[0138] Among them, to ensure L f The value of is positive and must satisfy the condition β2>1.

[0139] S4, taking the RUM system frequency deviation, output power, and transmission efficiency under variable load conditions as the objective functions in the multi-objective optimization model;

[0140] These two design variables offer greater potential for compensation network optimization. However, due to the large number of parameters and complex calculation formulas involved in high-order compensation networks and loosely coupled transformers, existing parameter design methods struggle to find a global optimal solution. Therefore, the present invention employs the NSGA-III optimization algorithm to globally optimize the design variables β1 and β2. Prior to optimization, a multi-objective optimization model must be established. This invention focuses on the system's three objective functions: frequency deviation, output power, and transmission efficiency.

[0141] S4.1. Based on the resonance condition of the primary equivalent circuit, the resonant frequency f of the RUM system is obtained. r1 The relationship between

[0142] set up and According to formula (6), the condition for the resonance of the primary circuit can be deduced as follows:

[0143]

[0144] Among them, in step S1, L P , L S 、M PS 、R P and R S The specific value of has been determined, the resonant angular frequency ω of the system r1 and the resonant frequency f r1 The compensation network parameters and the reflected impedance Z r The reflected impedance Z r Based on formula (5), it can be calculated;

[0145] S4.2. Smaller frequency deviation under load changes not only helps the ultrasonic vibrator maintain optimal working conditions, but also reduces reactive power loss. Therefore, calculate the resonant frequency f of the RUM system under m load conditions. r1 The resonance frequency f of the ultrasonic vibrator in series s The average frequency deviation between them is used as the evaluation function F1:

[0146]

[0147] Among them, f r1 (i) represents the resonant frequency of the RUM system under the i-th load condition, f s (i) represents the series resonant frequency of the ultrasonic vibrator under the i-th load condition.

[0148] S4.3. Based on Kirchhoff's current law, the current expression of each branch is obtained as shown in formula (14), and the output power P is obtained t The expression of transmission efficiency η is shown in formula (15);

[0149]

[0150] Among them, I in Indicates the system input current, U in Indicates the input voltage, I f Represents the current flowing through the first compensation capacitor, I P Represents the current flowing through the primary coil, I S Indicates the current flowing through the ultrasonic vibrator.

[0151]

[0152] S4.4, at input voltage U in is 50V and the operating frequency is f r1 Under the condition of m load conditions, the average output power is calculated as the evaluation function F2, and the expression is:

[0153]

[0154] Among them, P t (i) represents the output power of the RUM system under the i-th load condition.

[0155] S4.5. Calculate the average transmission efficiency of the RUM system under m load conditions as the evaluation function F3, which is expressed as:

[0156]

[0157] Where η(i) represents the transmission efficiency of the RUM system under the i-th load condition.

[0158] The evaluation function model is obtained as:

[0159]

[0160] S5. No-load resonant frequency matching, design variable range, and compensation component stress are used as constraints in the multi-objective optimization model;

[0161] No-load resonant frequency matching constraint: Under no-load conditions, i = 1, the RUM system is required to achieve resonant frequency matching with the ultrasonic vibrator, and the configuration of the compensation network parameters must meet Im(Z in [ω s (i=1)])=Im(Z s [ω s (i=1)])=0.

[0162] Design variable range constraints; in order to achieve a wide range of parameter space in the optimization process and comprehensively consider cost factors, set the compensation capacitor C P and C f The value range of is 0-500nF, and the corresponding design variables are defined as 1<β1<8.4, 1<β2<55.5.

[0163] Stress constraints of compensation components:

[0164] Combining equations (14) and (15), we can obtain the input voltage U when the ultrasonic vibrator works at the maximum power of 400W. in Should meet the following requirements:

[0165]

[0166] When the ultrasonic vibrator works at maximum power, the current stress of the compensation inductor and the voltage stress of each compensation capacitor are expressed as follows:

[0167]

[0168] Among them, I Lf To compensate the current stress of the inductor, U Cf is the voltage stress of the first compensation capacitor, U CP is the voltage stress of the second compensation capacitor, U Cs is the voltage stress of the third compensation capacitor.

[0169] To prevent damage to the compensation components due to overvoltage or overcurrent, and to ensure safe operation of the RUM system under variable load and maximum ultrasonic vibrator power conditions, the parameter design of the compensation components should be based on their specifications and take into account the safety margin. Specifically, the rated voltage U max Set to 800V; the compensation inductor is wound with 0.01×160 strands of Litz wire, and the maximum allowable current is I max Set to 8 A. The stress constraint function of the compensation element can be expressed as:

[0170]

[0171] Among them, I Lf (i) is the current stress of the compensation inductor under the i-th load condition, U Cf (i) is the voltage stress of the first compensation capacitor under the i-th load condition, U CP (i) is the voltage stress of the second compensation capacitor under the i-th load condition, U Cs (i) is the voltage stress of the third compensation capacitor under the i-th load condition.

[0172] S6. Determine the optimal design variables β1 and β2, and determine the optimal compensation network parameter combination.

[0173] The NSGA-III algorithm combines non-dominated sorting and reference point allocation, which can improve optimization performance and stability while maintaining solution diversity and uniform distribution. It is particularly suitable for high-dimensional multi-objective optimization problems.

[0174] The optimization process of the NSGA-III algorithm is as follows Figure 6 As shown. First, the population is randomly initialized within the value range of the compensation network parameters. Then, a constraint function check is performed on each solution to screen out feasible solutions that meet the constraints. Next, for the feasible solutions, the objective function value is calculated and non-dominated sorting is performed to divide the solutions into different sorting levels. On this basis, the solutions are grouped through a reference point allocation mechanism to guide the uniform distribution of the solution set in the multi-objective space. Subsequently, genetic operations such as crossover and mutation are used to generate a new offspring population, and environmental selection is performed in combination with the current population to retain solutions with good diversity and good convergence, and further optimize the solution set distribution. The optimization process continues until the preset number of evolutionary iterations is reached or a specific convergence condition is met. Finally, the Pareto solution set is output.

[0175] The Pareto solution set forms a three-dimensional scatter plot, such as Figure 7 shown.

[0176] The ideal point method is used to evaluate the Pareto solution set. The steps are as follows: select the optimal normalized value of each objective function from all solutions as the ideal point, calculate the Euclidean distance between the i-th candidate solution and the ideal point, and select the candidate solution closest to the ideal point as the optimal solution. The mathematical expression is:

[0177]

[0178] Among them, y i represents the Euclidean distance between the i-th candidate solution and the ideal point, is the normalized value of the ideal point of the j-th target, is the normalized value of the i-th candidate solution on the j-th target.

[0179] The optimal design variables and LCC-S compensation network parameters can be determined through the optimal solution. The specific values ​​are shown in Table 2 and Table 3.

[0180] Table 2. Optimal design variables and evaluation function values.

[0181]

[0182] Table 3. Optimized LCC-S compensation network parameters

[0183]

[0184] In order to verify the feasibility of the proposed LCC-S compensation network parameter optimization method for the rotary ultrasonic machining system, a variable load experimental platform was established in this embodiment. The experimental results are shown in Figure 2. Figure 8(a)-Figure 8(c) As shown, compared with the LCC-S compensation network based on the traditional fully resonant compensation network parameter design method (traditional LCC-S compensation network), the LCC-S compensation network designed based on the LCC-S compensation network parameter optimization method provided by the present invention (optimized LCC-S compensation network) exhibits significant advantages in resonant frequency matching stability within the load range of 0-150N, with the frequency deviation index reduced by 50.43%. In addition, the output power and transmission efficiency of the optimized LCC-S compensation network have smaller variations, showing stronger load adaptability, especially under heavy load conditions, showing higher transmission efficiency and output power.

[0185] like Figure 9 As shown, this embodiment discloses a LCC-S compensation network parameter optimization system for a rotary ultrasonic machining system, which is used to execute the above method and includes the following modules:

[0186] Equivalent parameter acquisition module: obtain the equivalent parameter primary side self-inductance L of the loosely coupled transformer P , secondary side self-inductance L S 、Mutual inductance PS , equivalent internal resistance R P And the equivalent internal resistance R S , as well as the equivalent electromechanical parameters of the ultrasonic vibrator under variable load conditions: dynamic inductance L1, dynamic capacitance C1, dynamic resistance R1 and static capacitance C0;

[0187] RUM system equivalent circuit model building module: builds the equivalent circuit model of the rotary ultrasonic machining RUM system including the LCC-S compensation network;

[0188] Compensation network parameter configuration module: configure LCC-S compensation network parameters;

[0189] Objective function determination module: The RUM system frequency deviation, output power, and transmission efficiency under variable load conditions are used as the objective functions of the multi-objective optimization model;

[0190] Constraint determination module: uses no-load resonant frequency matching, design variable range, and compensation component stress as constraints for the multi-objective optimization model;

[0191] Optimal parameter solving module: Determine the optimal design variables and solve the global optimal compensation parameter combination.

[0192] For other contents of this embodiment, please refer to the above method embodiment.

[0193] In summary, the proposed LCC-S compensation network parameter optimization method and system for the rotary ultrasonic machining system significantly reduce the resonant frequency deviation caused by load changes, improve the system transmission efficiency and output power stability under variable load conditions, and significantly improve the transmission efficiency and output power under heavy load conditions, meeting the requirements of rotary ultrasonic machining for load changes and high power requirements.

[0194] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for optimizing parameters of LCC-S compensation network in a rotary ultrasonic machining system, characterized in that: The following steps are involved: S1. Obtain the equivalent parameter of the loosely coupled transformer, the primary self-inductance L P , secondary side self-inductance L S 、Mutual inductance PS , equivalent internal resistance R P And the equivalent internal resistance R S , as well as the equivalent electromechanical parameters of the ultrasonic vibrator under variable load conditions: dynamic inductance L1, dynamic capacitance C1, dynamic resistance R1 and static capacitance C0; S2, constructing an equivalent circuit model of the rotary ultrasonic machining RUM system including the LCC-S compensation network; S3. Configure LCC-S compensation network parameters; S4, taking the RUM system frequency deviation, output power, and transmission efficiency under variable load conditions as the objective functions of the multi-objective optimization model; S5. No-load resonant frequency matching, design variable range, and compensation component stress are used as constraints for the multi-objective optimization model. S6. Determine the optimal design variables β1 and β2, and determine the optimal compensation network parameter combination; Step S2 is specifically as follows: S2.1, construct a structure including the third compensation capacitor C S The secondary side equivalent circuit model connected in series, the equivalent impedance Z of the secondary side equivalent circuit is obtained S The expression is: (1) Where j represents the imaginary unit, R t represents the equivalent resistance of the ultrasonic vibrator, X t represents the equivalent reactance of the ultrasonic vibrator, is the operating angular frequency; In the secondary side equivalent circuit model, when the operating angular frequency Resonant angular frequency in series with the ultrasonic vibrator When they are equal, the impedance of the ultrasonic vibrator is minimum and the amplitude is maximum; the series resonant angular frequency and the corresponding resonant frequency f s for: (2) S2.

2. Establish the primary side equivalent circuit model including the LCC-S compensation network and obtain the input impedance Z in The expression is: (3) Among them, L f To compensate for the inductance, C f is the first compensation capacitor, C P is the second compensation capacitor, X r is the reflected reactance, R r is the reflected resistance; Step S3 is as follows: S3.

1. Substitute equation (2) into equation (1) to obtain the third compensation capacitor C S The expression that satisfies the secondary circuit resonance condition is: (4) Among them, Im represents the imaginary part; S3.2, replace the primary side self-inductance L in the primary side equivalent circuit P , the second compensation capacitor C P , equivalent internal resistance R P and the reflected resistor R r The branch formed is equivalent to an RLC series branch. Let its equivalent impedance be Z1. s C that achieves resonance at P The value is recorded as C P1 ; Introduce the first design variable β1 and define C P The actual value of is: (5) in, ; S3.3, set the first compensation capacitor C f The equivalent impedance connected in parallel with the RLC series branch is denoted as Z2, and its expression is: (6) Among them, β1>1; S3.4, obtain the first compensation capacitor C that meets the resonance condition f The value of C f1 , and introduce the second design variable β2 to adjust the compensation capacitor C f The actual value of (7) in, ; S3.5, input impedance Z in By compensating inductor L f The inductive reactance is connected in series with the equivalent impedance Z2, L f The values ​​satisfy the following relationship: (8) Among them, β2>1.

2. A method for optimizing parameters of an LCC-S compensation network for a rotary ultrasonic machining system according to claim 1, characterized in that: Step S4 is specifically as follows: S4.

1. Based on the resonance condition of the primary equivalent circuit, the resonant frequency f of the RUM system is obtained. r1 The relationship between set up and , then according to formula (3), the resonance condition of the primary equivalent circuit is derived as follows: (9) Where Im represents the imaginary part; According to the resonance condition shown in formula (9), the resonant angular frequency ω of the system r1 and the resonant frequency f r1 The compensation network parameters and the reflected impedance Z r Decide; S4.

2. Calculate the resonant frequency f of the RUM system under m load conditions r1 The resonance frequency f of the ultrasonic vibrator in series s The average frequency deviation between them is used as the evaluation function F1: (10) Among them, f r1 (i) represents the resonant frequency of the RUM system under the i-th load condition, f s (i) represents the series resonant frequency of the ultrasonic vibrator under the i-th load condition; S4.

3. Based on Kirchhoff's current law, the current expression of each branch is obtained as shown in formula (11), and the output power P is obtained t and transmission efficiency The expression of is shown in formula (12); (11) Among them, I in Indicates the system input current, U in Indicates the input voltage, I f Represents the current flowing through the first compensation capacitor, I P Represents the current flowing through the primary coil, I S Represents the current flowing through the ultrasonic vibrator; (12) S4.4, at input voltage U in is 50V and the operating frequency is f r1 Under the condition of m load conditions, the average output power is calculated as the evaluation function F2, and the expression is: (13) Among them, P t (i) represents the output power of the RUM system under the i-th load condition; S4.

5. Calculate the average transmission efficiency of the RUM system under m load conditions as the evaluation function F3, which is expressed as: (14) Where η(i) represents the transmission efficiency of the RUM system under the i-th load condition; The evaluation function model is obtained as: (15)。 3. A method for optimizing parameters of an LCC-S compensation network for a rotary ultrasonic machining system as claimed in claim 2, characterized in that: Step S5 is specifically as follows: No-load resonant frequency matching constraint: Under no-load conditions, i=1, the RUM system is required to achieve resonant frequency matching with the ultrasonic vibrator, and the configuration of the compensation network parameters must meet ; Design variable range constraints; set compensation capacitor C P and C f The value range of is 0-500nF, and the corresponding design variables are defined as 1<β1<8.4, 1<β2<55.5; Compensation component stress constraints; based on the working conditions of variable load and ultrasonic vibrator maximum power of 400W, set the rated voltage U of the compensation capacitor max The maximum allowable current of the compensation inductor is 800V. max is 8A; the stress constraint function of the compensation element is: (16) Among them, I Lf (i) is the current stress of the compensation inductor under the i-th load condition, U Cf (i) is the voltage stress of the first compensation capacitor under the i-th load condition, U CP (i) is the voltage stress of the second compensation capacitor under the i-th load condition, U Cs (i) is the voltage stress of the third compensation capacitor under the i-th load condition.

4. A method for optimizing parameters of an LCC-S compensation network of a rotary ultrasonic machining system according to any one of claims 1 to 3, characterized in that: Step S6 is specifically as follows: determining the optimal design variables based on the NSGA-III optimization algorithm and the ideal point method, and determining the optimal compensation network parameter combination.

5. The method for optimizing parameters of the LCC-S compensation network of a rotary ultrasonic machining system according to claim 4, wherein: In step S6, the NSGA-III algorithm combines non-dominated sorting and reference point allocation to determine the Pareto solution set; The ideal point method is used to evaluate the Pareto solution set. Specifically, the optimal normalized value of each objective function is selected from all solutions as the ideal point. The Euclidean distance between the i-th candidate solution and the ideal point is calculated, and the candidate solution closest to the ideal point is selected as the optimal solution. The mathematical expression is: (17) Where, represents the Euclidean distance between the i-th candidate solution and the ideal point, is the normalized value of the ideal point of the j-th target, is the normalized value of the i-th candidate solution on the j-th index; The optimal design variables and LCC-S compensation network parameters are determined through the optimal solution.

6. A system for optimizing parameters of an LCC-S compensation network for a rotary ultrasonic machining system, for executing the method according to any one of claims 1 to 5, characterized in that: Includes the following modules: Equivalent parameter acquisition module: obtain the equivalent parameter primary side self-inductance L of the loosely coupled transformer P , secondary side self-inductance L S 、Mutual inductance PS , equivalent internal resistance R P And the equivalent internal resistance R S , as well as the equivalent electromechanical parameters of the ultrasonic vibrator under variable load conditions: dynamic inductance L1, dynamic capacitance C1, dynamic resistance R1 and static capacitance C0; RUM system equivalent circuit model building module: builds the equivalent circuit model of the rotary ultrasonic machining RUM system including the LCC-S compensation network; Compensation network parameter configuration module: configure LCC-S compensation network parameters; Objective function determination module: The RUM system frequency deviation, output power, and transmission efficiency under variable load conditions are used as the objective functions of the multi-objective optimization model; Constraint determination module: uses no-load resonant frequency matching, design variable range, and compensation component stress as constraints for the multi-objective optimization model; Optimal parameter solving module: Determine the optimal design variables and solve the global optimal compensation parameter combination.

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